Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function

[摘要] In the article, we present several new monotonicity properties and bounds involving the generalized Grötzsch ring functions $\mu _{a,b}$ in the theory of Ramanujan’s generalized modular equation for $0< a, b<1$. Our results are the variants and extensions of some previously known results.

[学科分类] 电力

[关键词] Gaussian hypergeometric function;Generalized Grötzsch ring function;Generalized elliptic integral;Monotonicity property